Problems of the Sensitivity Parameter and Its Relation to the Time-varying Fundamental Couplings Problems

TL;DR

This paper examines the limitations of the sensitivity parameter in quantifying fine-tuning, especially when relating dimensionful parameters to dimensionless couplings across energy scales, and proposes ways to improve its reliability.

Contribution

It identifies specific circumstances where the sensitivity parameter fails and suggests improved usage methods to enhance its reliability in theoretical physics.

Findings

Sensitivity parameter fails when relating parameters across energy scales.

High sensitivity of energy scale parameters affects the reliability of the sensitivity measure.

Proper use of the sensitivity parameter can mitigate these issues.

Abstract

The sensitivity parameter is widely used for quantifying fine tuning. However, examples show it fails to give correct results under certain circumstances. We argue that these problems only occur when calculating the sensitivity of a dimensionful mass parameter at one energy scale to the variation of a dimensionless coupling constant at another energy scale. Thus, by mechanisms such as dynamical symmetry breaking etc, the high sensitivity of the energy scale parameter (\Lambda) to the dimensionless coupling constant can affect the reliability of the sensitivity parameter through the renormalization invariant factor of the dimensionful parameter. Theoretically, These phenomena are similar to the problems associated with the time-varying coupling constant discovered recently. We argue that, the reliability of the sensitivity parameter can be improved if it is used properly.